Question 1.
How many grams of NaOH are needed to produce an aqueous solution with volume of 500 ml and pH of 9 ?
Question 2.
How many grams of H2SO4 (SULFURIC ACID) are needed to produce an aqueous solution with volume of 1L and pH of 4?
How many grams of NaOH are needed to produce an aqueous solution with volume of 500 ml and pH of 9?
Solution:
To calculate the amount of NaOH needed to produce a solution with a pH of 9, we first need to use the chemical reaction that occurs between NaOH and water:
\text{NaOH + H}_2\text{O} \rightarrow \text{Na}^+ + \text{OH}^- + \text{H}_2\text{O}
The hydroxide ion (OH-) from NaOH will react with water to produce more OH- ions, which will increase the pH of the solution. The pH of 9 indicates a basic solution, which means that the concentration of hydroxide ions (OH-) is higher than the concentration of hydrogen ions (H+). We can use the following equation to calculate the concentration of OH- ions:
p\text{OH} = 14 - \text{pH}
p\text{OH} is the negative logarithm of the hydroxide ion concentration, and pH is the negative logarithm of the hydrogen ion concentration.
p\text{OH} = 14 - 9 = 5
[\text{OH}^-] = 10^{-p\text{OH}} = 10^{-5} = 0.00001 \text{ M}
The molarity of NaOH needed to produce this concentration of hydroxide ions is the same as the concentration of hydroxide ions, since NaOH dissociates completely in water to produce one mole of OH- ions per mole of NaOH:
Molarity = [\text{OH}^-] = 0.00001 \text{ M}
Now we can use the molarity and volume of the solution to calculate the number of moles of NaOH needed:
Molarity = moles / volume
moles = Molarity x volume = 0.00001 x 0.5 = 0.000005 \text{ moles}$
The molar mass of NaOH is 40 g/mol, so the mass of NaOH needed is:
mass = moles x molar mass = 0.000005 x 40 = 0.0002 g or 0.2 mg
Therefore, \mathbf{0.2\ mg} of NaOH is needed to produce an aqueous solution with a volume of 500 ml and a pH of 9.
Question 2:
How many grams of H2SO4 (SULFURIC ACID) are needed to produce an aqueous solution with volume of 1L and pH of 4?
Solution:
Sulfuric acid (H2SO4) is a strong acid that dissociates completely in water to produce hydrogen ions (H+) and sulfate ions (SO4^-2):
\text{H}_2\text{SO}_4 \rightarrow 2\text{H}^+ + \text{SO}_4^{2-}
The pH of 4 indicates an acidic solution, which means that the concentration of hydrogen ions (H+) is higher than the concentration of hydroxide ions (OH-). We can use the following equation to calculate the concentration of hydrogen ions:
p\text{H} = -\log[\text{H}^+]
[\text{H}^+] = 10^{-p\text{H}} = 10^{-4} = 0.0001 \text{ M}
The molarity of sulfuric acid needed to produce this concentration of hydrogen ions is the same as the concentration of hydrogen ions, since sulfuric acid dissociate fully as a strong acid (same to the strong base)
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